English

On Postnikov completeness for replete topoi

Algebraic Topology 2025-04-15 v2 Algebraic Geometry

Abstract

We show that the hypercomplete \infty-topos associated with any replete topos is Postnikov complete, positively answering a question of Bhatt and Scholze; this will be deduced from the Milnor sequences for sheaves of spaces on replete topoi that we construct. As a corollary, we generalize a result of To\"en on affine stacks.

Cite

@article{arxiv.2210.14146,
  title  = {On Postnikov completeness for replete topoi},
  author = {Shubhodip Mondal and Emanuel Reinecke},
  journal= {arXiv preprint arXiv:2210.14146},
  year   = {2025}
}

Comments

Revision based on referee comments. 14 pages; comments still welcome

R2 v1 2026-06-28T04:28:56.374Z